A note on nil-clean rings-Reference-Cited by-同舟云学术

A note on nil-clean rings

Published:2020-11-01 Issue:2 Volume:12 Page:287-293
ISSN:2066-7752
Container-title:Acta Universitatis Sapientiae, Mathematica
language:en
Short-container-title:

Author:

Danchev Peter V.¹

Affiliation:

1. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences , “Acad. G. Bonchev” str., bl. 8, 1113 Sofia , Bulgaria

Abstract

Abstract We study a special kind of nil-clean rings, namely those nil-clean rings whose nilpotent elements are difference of two “left-right symmetric” idempotents, and prove that in some various cases they are strongly π-regular. We also show that all nil-clean rings having cyclic unit 2-groups are themselves strongly nil-clean of characteristic 2 (and thus they are again strongly π-regular).

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.sciendo.com/pdf/10.2478/ausm-2020-0020

Reference11 articles.

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2. [2] S. Breaz, G. Călugăreanu, P. Danchev and T. Micu, Nil-clean matrix rings, Linear Algebra and Appl., (10) 439 (2013), 3115–3119.

3. [3] P. V. Danchev, Weakly exchange rings whose units are sums of two idempotents, Vestnik St. Petersburg Univ., Math., Mech. & Astronomy, (2) 6 (64) (2019), 265–269.

4. [4] P. V. Danchev and T. Y. Lam, Rings with unipotent units, Publ. Math. Debrecen, (3-4) 88 (2016), 449–466.

5. [5] P. Danchev and J. Matczuk, n-Torsion clean rings, Contemp. Math., 727 (2019), 71–82.

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1. Strongly 2-Nil Clean Rings with Units of Order Two;European Journal of Pure and Applied Mathematics;2023-07-30